We could even go as far as mentioning Selphie from FF8 and Aerith from FF7. Their limit breaks were more so for healing, but the materia / junction systems allowed them to cast Black Magic or even Ultima if they really wanted to.

FF6 pretty much had Terra and Celes as the natural magic users without learning from Espers and they even had fire, ice, Ultima and Meteor. Strago could count too as a "healer" using Blue Magic (Lore) and having Grand Delta (Train).